9. Let R be a relation on N defined by (x, y) e Riff there is a prime p such that y = px. Describe in words the reflexive, symmetric and transitive closures of R, denoted by r, s and t, respectively. (a) Which of the following are true: 2 r(s(R)) = s(r(R)) r(t(R)) = t(r(R)) s(t(R)) = t(s(R)) You need to justify your answer. (b) Which of them hold for all relations on N? (c) Using the reflexive, symmetric, and transitive closures, express the smallest equivalence relation containing an arbitrary relation. (d) What is the smallest partial order containing R?